1893.] Experiments on the Reflection of Light. 73 



In fig. 2, the observer is supposed to be looking through an 

 analyser at the point of incidence along the reflected ray ; if 



Fig. 2. 



therefore the analyser be placed in the position of extinction Ot], 

 and be then turned through a very small angle 6 towards the 

 right hand of the observer, the emergent vibration will be 



- ^ sin ^ + -J? cos ^ = ^^ cos (^ + e,) - Q- (P cos ^ + Q sin ^), 



since 6 is very small. Whence the intensity I^ of the emergent 

 light is 



P = ^-^e' - mq (P cos e, - Q sin e,) 6 + q' (P^ + Q^) . . .(9). 



If we put 1=0, this is a quadratic equation for determining 

 the values of 6 for which the intensity vanishes, and we see that 

 both roots must be of the same sign ; also both will be positive 

 provided the coefficient of 6 in the second term be positive*. If 

 therefore q be positive, this condition will be satisfied provided 



P cos gj — Q sin e^ > (10). 



Omitting the extraneous factors in (7), which are positive, the 

 condition becomes 



M cos^ i sin (2a — e^) + Rc^ sin (2a — '2u — ej + c cos i sin (3a — u — e^ 



+ R^c cos i sin (a — ^^ — ej > , . .(11). 



Taking the values of R and a furnished by Sir J. Conroy's 

 observations of the principal incidence and azimuth, it can be 

 shewn by actual calculation that this inequality is always satisfied. 

 From [7] it at once follows that u = at normal incidence, and 

 I find that at grazing incidence u = \°'?>^' about; u is therefore 

 an exceedingly small positive angle. At grazing incidence e^ = 0, 

 whilst at normal incidence I find by calculation from (8) that 



e, = 22° 48'. 



* The last term of (9) is so small that it may generally be omitted ; at the same 

 time the first experiment described on p. 385 of my book shews that it is capable of 

 producing a sensible effect. 



VOL. VIII. PT. II. 6 



